I figured it out, and SELinux is the difference. That is, SELinux on the HAProxy host (not a cluster node):
"SELinux only allows the web server to make outbound connections to a limited set of ports"
That is, you can't make an outbound http request to any port in the NodePort range (30000-32768) without opening that port on the "client", which is the HAProxy server in this case.
sudo semanage port --add --type http_port_t --proto tcp 30080
More specifically, I guess, the security context that HAProxy runs under is different than curl.